Using the Einstein field equations (REF ) and (REF ), it has
been explicitly proved [1]} that the black-hole null
circular geodesics are characterized by the relation [2]}
\({\cal N}(r)\equiv 3\mu (r)-1-8\pi r^2p(r)=0\ \ \ \ \text{for}\ \ \ \ r=r_{\gamma }\ .\) 
